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Discrete Math and Analyzing Social Graphs
Week 3
Finding probabilities using rules

QuizQuiz • 10 min10 minutes

Finding probabilities using rules

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Due DateMar 9, 3:59 AM EDTMarch 9, 3:59 AM EDT

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Finding probabilities using rules

Graded Quiz • 10 min

Due Mar 9, 3:59 AM EDT

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Finding probabilities using rules

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1.

Question 1

Let $A$ and $B$ be some events defined on the same probability space. Assume we know that $P(A)=1/2$ , $P(B)=1/3$ and $P(A\cup B)=2/3$ . Find $P(A\cap B)$ (as a proper fraction).

1 / 1 point

\frac{1}{6}

1 / 6

Correct

According to rule of sum of probabilities, $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ . Therefore, $P(A\cap B) = P(A) + P(B) - P(A\cup B)=1/2 + 1/3 - 2/3=1/6$ .

2.

Question 2

A fair dice rolled three times. What is the probability that "6" occurred at least once during this rollings?

1 / 1 point

\frac{91}{216}

1-125/216

Correct

Complement event is "6" never occurred. Its probability is $5^3/6^3$ . The probablity of our event is $1-5^3/6^3=91/216$ .